{
  "chapter": "c17", "claim_id": "c17-update-norm-001", "hardware_claim_boundary": "Deterministic matrix calculation; no optimizer throughput or end-task efficiency claim.", "harness_ref": "ch-17", "harness_wheel_sha256": "12b89a5ae1f68e234bc0dce02bd42f13acb35781aafcc78068d94c3a68018d60", "hypothesis": "Changing the update norm changes the steepest matrix direction.", "payload_sha256": "e38a64cb71e42d4d9af035e90fb2a427536e9ccf4bac92cbd10bc71cc4bc45c0", "phenomenon_id": "c17-norm-chooses-update", "provenance_class": "a", "schema_version": 1,
  "result": {"approximation_error": 0.0009394554194697147, "gradient_singular_values": [9.0, 3.0, 1.0, 0.2], "inner_products": {"frobenius": -9.54148835350125, "nuclear": -9.0, "operator": -13.2}, "newton_schulz_residuals": [1.6737661817344787, 1.605270455163879, 1.497827166801991, 1.367218780519799, 1.2471253315920905, 1.1124751153800625, 0.9781360352531825, 0.8816272653122567, 0.7513093181695729, 0.5293668467676398, 0.2472579635626635, 0.04963149706490222, 0.001878028262454312], "polar_singular_values": [1.0, 1.0, 1.0, 1.0]}
}